Question

Calculate the resistance of a piece of aluminum wire with a diameter of 100 mils and a length of two miles, at 68°F. Hint: Be sure to first convert mils to cmils and use the K value for aluminum found in the reference. (Round the FINAL answer to two decimal places.)

Answer 1

First you need to know the formula of the Resistance(R) of a conductor, which is:

$R = \frac{K*L}{CM}$ -- (A)

Where,
R = Resistance of the wire = ?
K = Specific resistance of the wire(In this case Aluminum at 68°F) = 17.02 ohm-circular-mil-foot
L = Length of the wire(in feet)
CM = Circular mil Area(In inches)


Now in order to use the above formula(A), we have to first convert TWO quantities:
1) The length of the wire(from miles to feet)
2) Mils to Circular mil Area

1.
The length of the wire given = 2 miles
The length of the wire(In feet) = 10560 ft
2.
Since the mils given = 100 mils.
Therefore,
Circular mils(Circular mil Area) = mils x mils = 100 x 100 = 10000 

Now plug-in the values in equation(A):

A=> R = $\frac{17.02 * 10560}{10000 }$

R = 17.97 ohms 

Ans: Resistance of the aluminum wire = 17.97 ohms.

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